It is proposed to develop efficient computational algorithms which will permit comprehensive mathematical modelling of the kidney. At present we have models of one or two solutes; this essentially means that we can solve mass balance equations for fifty to one hundred spacial compartments in the renal medulla. Extension of the efficiency of our algorithms has permitted us to handle approximately twice the complexity and ultimately we hope to increase the complexity by a factor of five to ten. This will enable us to include models of considerable spacial complexity (e.g., both the cortex and the medulla), include additional solutes, and/or pressure. We plan to study the available algorithms (including those developed by the principal investigator) for function minimization, computations involving sparse matrices, and improvement of conditioning and resolution in the solution of linear systems. It is reasonable to predict that these algorithms can be integrated and extended to develop efficient computational algorithms for our purposes.